Flip 3 coins, P(at least 2 heads) Step by Step

Step by step

The question

Question: 3 coins are flipped.

What is the probability of getting at least 2 heads?

The probability is a fraction: the outcomes we want, over all the outcomes.

P(at least 2 heads) = we wantall

P stands for probability.

P = probability

1 List all outcomes

Each coin lands heads, H, or tails, T.

Here is every outcome.

Each coin has 2 ways.

2 times 2 times 2 is 8 outcomes, all just as likely.

all = 2 × 2 × 2 = 8

This list of all the outcomes is called the sample space.

H = heads, T = tails

sample space = all the outcomes

2 Count the ones we want

Outcomes with at least 2 heads: HHH, HHT, HTH and THH.

That is 4 outcomes we want.

we want = 4

3 Write the fraction

4 we want, out of 8.

So the probability is 4/8.

P(at least 2 heads) = 48

Careful!

The order counts: the first and the second are different.

Careful: HT and TH are two outcomes

4 Simplify

Both 4 and 8 can be divided by 4.

That makes it simpler.

P(at least 2 heads) = 4 ÷ 48 ÷ 4

So it is 1/2.

P(at least 2 heads) = 12

5 Check

Let's check with the others.

8 minus 4 is 4.

4/8 plus 4/8 is 8/8: that is 1, all of them.

So the answer is right!

P(at least 2 heads) + P(not at least 2 heads) = 48 + 48 = 88 = 1

Let's look back.

First: list all outcomes.

Then: count the ones we want.

Then: write the fraction.

Then: simplify.

Last: check.

Answer